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Chords of miracle

Edit 7 18 …
Below are listed the dyadic chords of 11-limit miracle temperament. They are listed in order of increasing Graham complexity, with hash complexity used to break ties. For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2^s for all s∊S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "Hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity. The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal. The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord, so that if for example it says "werckismic" only 441/440 needs to be tempered out. Also, "marvel" denotes 9 odd limit (7-limit) marvel, whereas "unimarvel" means 11-limit marvel. The generator used below is the standard choice for miracle temperament, the secor. 16/15~15/14. However, it should be noted that the choice of generator does not effect the list of chords, only how those chords are interpreted. Does 0-7-13 denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.

Triads

Each of the triads below has three "inversions", i.e., can be written starting on any one of the three tones in the triad.

Note that the tones in the triad are noted in order of generator steps, not pitch. For example, look at triad #21. 1/1 - 8/5 - 6/5 is listed in order of generator steps, 0 - 7 - 13. Seven generator steps, or 8/5, is 813.7 cents. Thirteen generator steps, or 6/5, is 315.6 cents. If you put the triad in pitch order, you get 1/1 - 6/5 - 8/5, or 0.0 - 315.6 - 813.7 cents.

Also note that you won't see the traditional five-limit major triad, 1/1 - 5/4 - 3/2 in this list. That's because this list contains an inversion of the five-limit major triad: number 21. 1/1 - 6/5 - 8/5 is the first inversion of 1/1 - 5/4 - 3/2. In other words, to get the major chord from the list below, you need to take the second inversion of triad 21. The same may be true of other triads you're interested in.

All three inversions for all 63 chords are notated in this PDF (uses 41 EDO sagittal notation) and can be heard using piano, oud, or sine wave timbres (all links in MP3 format and tuned to 41 EDO). Finally, here is a tuned MIDI file. The sequence is: chord as outlined in the list below, first inversion, second inversion, quarter-note rest.
Number
 Chord
 Transversal
 Type
 Hash
1
 0-2-5
 1-8/7-7/5
 werckismic
 5.209453
2
 0-3-5
 1-11/9-7/5
 werckismic
 5.357552
3
 0-3-6
 1-11/9-3/2
 rastmic
 6.189825
4
 0-2-7
 1-8/7-8/5
 utonal
 7.055282
5
 0-5-7
 1-7/5-8/5
 otonal
 7.330917
6
 0-2-8
 1-8/7-12/7
 otonal
 8.027906
7
 0-3-8
 1-11/9-12/7
 swetismic
 8.049849
8
 0-5-8
 1-7/5-12/7
 swetismic
 8.174926
9
 0-6-8
 1-3/2-12/7
 utonal
 8.326429
10
 0-2-9
 1-8/7-11/6
 keenanismic
 9.014020
11
 0-3-9
 1-11/9-11/6
 utonal
 9.025140
12
 0-6-9
 1-3/2-11/6
 otonal
 9.172428
13
 0-7-9
 1-8/5-11/6
 keenanismic
 9.324181
14
 0-3-12
 1-11/9-9/8
 rastmic
 12.003167
15
 0-5-12
 1-7/5-9/8
 marvel
 12.011577
16
 0-6-12
 1-3/2-9/8
 ambitonal
 12.022715
17
 0-7-12
 1-8/5-9/8
 marvel
 12.044736
18
 0-9-12
 1-11/6-9/8
 rastmic
 12.170238
19
 0-5-13
 1-7/5-6/5
 otonal
 13.005800
20
 0-6-13
 1-3/2-6/5
 utonal
 13.011402
21
 0-7-13
 1-8/5-6/5
 otonal
 13.022541
22
 0-8-13
 1-12/7-6/5
 utonal
 13.044565
23
 0-2-14
 1-8/7-9/7
 otonal
 14.000440
24
 0-5-14
 1-7/5-9/7
 swetismic
 14.002903
25
 0-6-14
 1-3/2-9/7
 utonal
 14.005712
26
 0-7-14
 1-8/5-9/7
 marvel
 14.011315
27
 0-8-14
 1-12/7-9/7
 otonal
 14.022455
28
 0-9-14
 1-11/6-9/7
 swetismic
 14.04448
29
 0-12-14
 1-9/8-9/7
 utonal
 14.321999
30
 0-2-15
 1-8/7-11/8
 keenanismic
 15.000220
31
 0-3-15
 1-11/9-11/8
 utonal
 15.000396
32
 0-6-15
 1-3/2-11/8
 otonal
 15.002859
33
 0-7-15
 1-8/5-11/8
 keenanismic
 15.005660
34
 0-8-15
 1-12/7-11/8
 keenanismic
 15.011271
35
 0-9-15
 1-11/6-11/8
 utonal
 15.022411
36
 0-12-15
 1-9/8-11/8
 otonal
 15.169964
37
 0-13-15
 1-6/5-11/8
 keenanismic
 15.321963
38
 0-2-17
 1-8/7-11/7
 otonal
 17.000055
39
 0-3-17
 1-11/9-11/7
 utonal
 17.000099
40
 0-5-17
 1-7/5-11/7
 werckismic
 17.000363
41
 0-8-17
 1-12/7-11/7
 otonal
 17.002826
42
 0-9-17
 1-11/6-11/7
 utonal
 17.005636
43
 0-12-17
 1-9/8-11/7
 werckismic
 17.0444
44
 0-14-17
 1-9/7-11/7
 otonal
 17.169935
45
 0-15-17
 1-11/8-11/7
 utonal
 17.321937
46
 0-2-19
 1-8/7-9/5
 werckismic
 19.000014
47
 0-5-19
 1-7/5-9/5
 otonal
 19.000091
48
 0-6-19
 1-3/2-9/5
 utonal
 19.000179
49
 0-7-19
 1-8/5-9/5
 otonal
 19.000355
50
 0-12-19
 1-9/8-9/5
 utonal
 19.011230
51
 0-13-19
 1-6/5-9/5
 otonal
 19.022371
52
 0-14-19
 1-9/7-9/5
 utonal
 19.044397
53
 0-17-19
 1-11/7-9/5
 werckismic
 19.321930
54
 0-3-22
 1-11/9-11/10
 utonal
 22.000003
55
 0-5-22
 1-7/5-11/10
 otonal
 22.000011
56
 0-7-22
 1-8/5-11/10
 otonal
 22.000044
57
 0-8-22
 1-12/7-11/10
 swetismic
 22.000088
58
 0-9-22
 1-11/6-11/10
 utonal
 22.000176
59
 0-13-22
 1-6/5-11/10
 otonal
 22.002815
60
 0-14-22
 1-9/7-11/10
 swetismic
 22.005625
61
 0-15-22
 1-11/8-11/10
 utonal
 22.011228
62
 0-17-22
 1-11/7-11/10
 utonal
 22.044394
63
 0-19-22
 1-9/5-11/10
 otonal
 22.169925

Tetrads

Number
 Chord
 Transversal
 Type
 Hash
1
 0-2-5-7
 1-8/7-7/5-8/5
 werckismic
 7.366322
2
 0-2-5-8
 1-8/7-7/5-12/7
 jove
 8.194757
3
 0-3-5-8
 1-11/9-7/5-12/7
 jove
 8.214319
4
 0-3-6-8
 1-11/9-3/2-12/7
 jove
 8.361944
5
 0-3-6-9
 1-11/9-3/2-11/6
 rastmic
 9.192293
6
 0-2-7-9
 1-8/7-8/5-11/6
 keenanismic
 9.333155
7
 0-3-5-12
 1-11/9-7/5-9/8
 miracle
 12.014369
8
 0-3-6-12
 1-11/9-3/2-9/8
 rastmic
 12.025486
9
 0-5-7-12
 1-7/5-8/5-9/8
 marvel
 12.055621
10
 0-3-9-12
 1-11/9-11/6-9/8
 rastmic
 12.172740
11
 0-6-9-12
 1-3/2-11/6-9/8
 rastmic
 12.190133
12
 0-7-9-12
 1-8/5-11/6-9/8
 miracle
 12.209758
13
 0-5-7-13
 1-7/5-8/5-6/5
 otonal
 13.028079
14
 0-5-8-13
 1-7/5-12/7-6/5
 swetismic
 13.050019
15
 0-6-8-13
 1-3/2-12/7-6/5
 utonal
 13.055452
16
 0-2-5-14
 1-8/7-7/5-9/7
 jove
 14.003254
17
 0-2-7-14
 1-8/7-8/5-9/7
 marvel
 14.011664
18
 0-5-7-14
 1-7/5-8/5-9/7
 unimarvel
 14.014108
19
 0-2-8-14
 1-8/7-12/7-9/7
 otonal
 14.022801
20
 0-5-8-14
 1-7/5-12/7-9/7
 swetismic
 14.025226
21
 0-6-8-14
 1-3/2-12/7-9/7
 ambitonal
 14.027992
22
 0-2-9-14
 1-8/7-11/6-9/7
 unimarvel
 14.044821
23
 0-6-9-14
 1-3/2-11/6-9/7
 swetismic
 14.049934
24
 0-7-9-14
 1-8/5-11/6-9/7
 unimarvel
 14.055367
25
 0-5-12-14
 1-7/5-9/8-9/7
 unimarvel
 14.324251
26
 0-6-12-14
 1-3/2-9/8-9/7
 utonal
 14.326500
27
 0-7-12-14
 1-8/5-9/8-9/7
 marvel
 14.330987
28
 0-9-12-14
 1-11/6-9/8-9/7
 jove
 14.357621
29
 0-3-6-15
 1-11/9-3/2-11/8
 rastmic
 15.003210
30
 0-2-7-15
 1-8/7-8/5-11/8
 keenanismic
 15.005844
31
 0-2-8-15
 1-8/7-12/7-11/8
 keenanismic
 15.011446
32
 0-3-8-15
 1-11/9-12/7-11/8
 unimarvel
 15.011620
33
 0-6-8-15
 1-3/2-12/7-11/8
 keenanismic
 15.014064
34
 0-2-9-15
 1-8/7-11/6-11/8
 keenanismic
 15.022585
35
 0-3-9-15
 1-11/9-11/6-11/8
 utonal
 15.022758
36
 0-6-9-15
 1-3/2-11/6-11/8
 ambitonal
 15.025183
37
 0-7-9-15
 1-8/5-11/6-11/8
 keenanismic
 15.027949
38
 0-3-12-15
 1-11/9-9/8-11/8
 rastmic
 15.170277
39
 0-6-12-15
 1-3/2-9/8-11/8
 otonal
 15.172467
40
 0-7-12-15
 1-8/5-9/8-11/8
 unimarvel
 15.174965
41
 0-9-12-15
 1-11/6-9/8-11/8
 rastmic
 15.189863
42
 0-6-13-15
 1-3/2-6/5-11/8
 keenanismic
 15.324216
43
 0-7-13-15
 1-8/5-6/5-11/8
 keenanismic
 15.326465
44
 0-8-13-15
 1-12/7-6/5-11/8
 keenanismic
 15.330952
45
 0-2-5-17
 1-8/7-7/5-11/7
 werckismic
 17.000407
46
 0-3-5-17
 1-11/9-7/5-11/7
 werckismic
 17.000451
47
 0-2-8-17
 1-8/7-12/7-11/7
 otonal
 17.002870
48
 0-3-8-17
 1-11/9-12/7-11/7
 swetismic
 17.002914
49
 0-5-8-17
 1-7/5-12/7-11/7
 jove
 17.003177
50
 0-2-9-17
 1-8/7-11/6-11/7
 keenanismic
 17.005679
51
 0-3-9-17
 1-11/9-11/6-11/7
 utonal
 17.005723
52
 0-3-12-17
 1-11/9-9/8-11/7
 jove
 17.044490
53
 0-5-12-17
 1-7/5-9/8-11/7
 prodigy
 17.044746
54
 0-9-12-17
 1-11/6-9/8-11/7
 jove
 17.049859
55
 0-2-14-17
 1-8/7-9/7-11/7
 otonal
 17.169974
56
 0-5-14-17
 1-7/5-9/7-11/7
 jove
 17.170248
57
 0-8-14-17
 1-12/7-9/7-11/7
 otonal
 17.172437
58
 0-9-14-17
 1-11/6-9/7-11/7
 swetismic
 17.174935
59
 0-12-14-17
 1-9/8-9/7-11/7
 werckismic
 17.209463
60
 0-2-15-17
 1-8/7-11/8-11/7
 keenanismic
 17.321972
61
 0-3-15-17
 1-11/9-11/8-11/7
 utonal
 17.322007
62
 0-8-15-17
 1-12/7-11/8-11/7
 keenanismic
 17.324189
63
 0-9-15-17
 1-11/6-11/8-11/7
 utonal
 17.326438
64
 0-12-15-17
 1-9/8-11/8-11/7
 werckismic
 17.357561
65
 0-2-5-19
 1-8/7-7/5-9/5
 werckismic
 19.000102
66
 0-2-7-19
 1-8/7-8/5-9/5
 werckismic
 19.000366
67
 0-5-7-19
 1-7/5-8/5-9/5
 otonal
 19.000443
68
 0-5-12-19
 1-7/5-9/8-9/5
 marvel
 19.011317
69
 0-6-12-19
 1-3/2-9/8-9/5
 utonal
 19.011405
70
 0-7-12-19
 1-8/5-9/8-9/5
 marvel
 19.011579
71
 0-5-13-19
 1-7/5-6/5-9/5
 otonal
 19.022457
72
 0-6-13-19
 1-3/2-6/5-9/5
 ambitonal
 19.022544
73
 0-7-13-19
 1-8/5-6/5-9/5
 otonal
 19.022717
74
 0-2-14-19
 1-8/7-9/7-9/5
 werckismic
 19.044407
75
 0-5-14-19
 1-7/5-9/7-9/5
 swetismic
 19.044482
76
 0-6-14-19
 1-3/2-9/7-9/5
 utonal
 19.044568
77
 0-7-14-19
 1-8/5-9/7-9/5
 marvel
 19.044738
78
 0-12-14-19
 1-9/8-9/7-9/5
 utonal
 19.055285
79
 0-2-17-19
 1-8/7-11/7-9/5
 werckismic
 19.321939
80
 0-5-17-19
 1-7/5-11/7-9/5
 werckismic
 19.322001
81
 0-12-17-19
 1-9/8-11/7-9/5
 werckismic
 19.330919
82
 0-14-17-19
 1-9/7-11/7-9/5
 werckismic
 19.357554
83
 0-3-5-22
 1-11/9-7/5-11/10
 werckismic
 22.000014
84
 0-5-7-22
 1-7/5-8/5-11/10
 otonal
 22.000055
85
 0-3-8-22
 1-11/9-12/7-11/10
 swetismic
 22.000091
86
 0-5-8-22
 1-7/5-12/7-11/10
 swetismic
 22.000099
87
 0-3-9-22
 1-11/9-11/6-11/10
 utonal
 22.000179
88
 0-7-9-22
 1-8/5-11/6-11/10
 keenanismic
 22.000220
89
 0-5-13-22
 1-7/5-6/5-11/10
 otonal
 22.002826
90
 0-7-13-22
 1-8/5-6/5-11/10
 otonal
 22.002859
91
 0-8-13-22
 1-12/7-6/5-11/10
 swetismic
 22.002903
92
 0-5-14-22
 1-7/5-9/7-11/10
 swetismic
 22.005636
93
 0-7-14-22
 1-8/5-9/7-11/10
 unimarvel
 22.005669
94
 0-8-14-22
 1-12/7-9/7-11/10
 swetismic
 22.005713
95
 0-9-14-22
 1-11/6-9/7-11/10
 swetismic
 22.005800
96
 0-3-15-22
 1-11/9-11/8-11/10
 utonal
 22.011230
97
 0-7-15-22
 1-8/5-11/8-11/10
 keenanismic
 22.011271
98
 0-8-15-22
 1-12/7-11/8-11/10
 unimarvel
 22.011315
99
 0-9-15-22
 1-11/6-11/8-11/10
 utonal
 22.011402
100
 0-13-15-22
 1-6/5-11/8-11/10
 keenanismic
 22.014021
101
 0-3-17-22
 1-11/9-11/7-11/10
 utonal
 22.044397
102
 0-5-17-22
 1-7/5-11/7-11/10
 werckismic
 22.044405
103
 0-8-17-22
 1-12/7-11/7-11/10
 swetismic
 22.044480
104
 0-9-17-22
 1-11/6-11/7-11/10
 utonal
 22.044565
105
 0-14-17-22
 1-9/7-11/7-11/10
 swetismic
 22.049849
106
 0-15-17-22
 1-11/8-11/7-11/10
 utonal
 22.055283
107
 0-5-19-22
 1-7/5-9/5-11/10
 otonal
 22.169935
108
 0-7-19-22
 1-8/5-9/5-11/10
 otonal
 22.169964
109
 0-13-19-22
 1-6/5-9/5-11/10
 otonal
 22.172428
110
 0-14-19-22
 1-9/7-9/5-11/10
 swetismic
 22.174926
111
 0-17-19-22
 1-11/7-9/5-11/10
 werckismic
 22.209454

Pentads

Number
 Chord
 Transversal
 Type
 Hash
1
 0-3-6-9-12
 1-11/9-3/2-11/6-9/8
 rastmic
 12.192601
2
 0-2-5-7-14
 1-8/7-7/5-8/5-9/7
 miracle
 14.014456
3
 0-2-5-8-14
 1-8/7-7/5-12/7-9/7
 jove
 14.025572
4
 0-2-7-9-14
 1-8/7-8/5-11/6-9/7
 unimarvel
 14.055706
5
 0-5-7-12-14
 1-7/5-8/5-9/8-9/7
 unimarvel
 14.333225
6
 0-6-9-12-14
 1-3/2-11/6-9/8-9/7
 jove
 14.362012
7
 0-7-9-12-14
 1-8/5-11/6-9/8-9/7
 miracle
 14.366391
8
 0-3-6-8-15
 1-11/9-3/2-12/7-11/8
 miracle
 15.014413
9
 0-3-6-9-15
 1-11/9-3/2-11/6-11/8
 rastmic
 15.025529
10
 0-2-7-9-15
 1-8/7-8/5-11/6-11/8
 keenanismic
 15.028122
11
 0-3-6-12-15
 1-11/9-3/2-9/8-11/8
 rastmic
 15.172779
12
 0-3-9-12-15
 1-11/9-11/6-9/8-11/8
 rastmic
 15.190172
13
 0-6-9-12-15
 1-3/2-11/6-9/8-11/8
 rastmic
 15.192331
14
 0-7-9-12-15
 1-8/5-11/6-9/8-11/8
 miracle
 15.194795
15
 0-6-8-13-15
 1-3/2-12/7-6/5-11/8
 keenanismic
 15.333190
16
 0-2-5-8-17
 1-8/7-7/5-12/7-11/7
 jove
 17.003221
17
 0-3-5-8-17
 1-11/9-7/5-12/7-11/7
 jove
 17.003265
18
 0-3-5-12-17
 1-11/9-7/5-9/8-11/7
 miracle
 17.044832
19
 0-3-9-12-17
 1-11/9-11/6-9/8-11/7
 jove
 17.049944
20
 0-2-5-14-17
 1-8/7-7/5-9/7-11/7
 jove
 17.170287
21
 0-2-8-14-17
 1-8/7-12/7-9/7-11/7
 otonal
 17.172476
22
 0-5-8-14-17
 1-7/5-12/7-9/7-11/7
 jove
 17.172750
23
 0-2-9-14-17
 1-8/7-11/6-9/7-11/7
 unimarvel
 17.174974
24
 0-5-12-14-17
 1-7/5-9/8-9/7-11/7
 miracle
 17.209767
25
 0-9-12-14-17
 1-11/6-9/8-9/7-11/7
 jove
 17.214329
26
 0-2-8-15-17
 1-8/7-12/7-11/8-11/7
 keenanismic
 17.324225
27
 0-3-8-15-17
 1-11/9-12/7-11/8-11/7
 unimarvel
 17.324260
28
 0-2-9-15-17
 1-8/7-11/6-11/8-11/7
 keenanismic
 17.326473
29
 0-3-9-15-17
 1-11/9-11/6-11/8-11/7
 utonal
 17.326508
30
 0-3-12-15-17
 1-11/9-9/8-11/8-11/7
 jove
 17.357629
31
 0-9-12-15-17
 1-11/6-9/8-11/8-11/7
 jove
 17.361952
32
 0-2-5-7-19
 1-8/7-7/5-8/5-9/5
 werckismic
 19.000454
33
 0-5-7-12-19
 1-7/5-8/5-9/8-9/5
 marvel
 19.011667
34
 0-5-7-13-19
 1-7/5-8/5-6/5-9/5
 otonal
 19.022804
35
 0-2-5-14-19
 1-8/7-7/5-9/7-9/5
 jove
 19.044493
36
 0-2-7-14-19
 1-8/7-8/5-9/7-9/5
 prodigy
 19.044749
37
 0-5-7-14-19
 1-7/5-8/5-9/7-9/5
 unimarvel
 19.044824
38
 0-5-12-14-19
 1-7/5-9/8-9/7-9/5
 unimarvel
 19.055370
39
 0-6-12-14-19
 1-3/2-9/8-9/7-9/5
 utonal
 19.055455
40
 0-7-12-14-19
 1-8/5-9/8-9/7-9/5
 marvel
 19.055624
41
 0-2-5-17-19
 1-8/7-7/5-11/7-9/5
 werckismic
 19.322010
42
 0-5-12-17-19
 1-7/5-9/8-11/7-9/5
 prodigy
 19.330989
43
 0-2-14-17-19
 1-8/7-9/7-11/7-9/5
 werckismic
 19.357563
44
 0-5-14-17-19
 1-7/5-9/7-11/7-9/5
 jove
 19.357623
45
 0-12-14-17-19
 1-9/8-9/7-11/7-9/5
 werckismic
 19.366324
46
 0-3-5-8-22
 1-11/9-7/5-12/7-11/10
 jove
 22.000102
47
 0-5-7-13-22
 1-7/5-8/5-6/5-11/10
 otonal
 22.002870
48
 0-5-8-13-22
 1-7/5-12/7-6/5-11/10
 swetismic
 22.002914
49
 0-5-7-14-22
 1-7/5-8/5-9/7-11/10
 unimarvel
 22.005680
50
 0-5-8-14-22
 1-7/5-12/7-9/7-11/10
 swetismic
 22.005724
51
 0-7-9-14-22
 1-8/5-11/6-9/7-11/10
 unimarvel
 22.005844
52
 0-3-8-15-22
 1-11/9-12/7-11/8-11/10
 unimarvel
 22.011318
53
 0-3-9-15-22
 1-11/9-11/6-11/8-11/10
 utonal
 22.011405
54
 0-7-9-15-22
 1-8/5-11/6-11/8-11/10
 keenanismic
 22.011446
55
 0-7-13-15-22
 1-8/5-6/5-11/8-11/10
 keenanismic
 22.014064
56
 0-8-13-15-22
 1-12/7-6/5-11/8-11/10
 unimarvel
 22.014108
57
 0-3-5-17-22
 1-11/9-7/5-11/7-11/10
 werckismic
 22.044408
58
 0-3-8-17-22
 1-11/9-12/7-11/7-11/10
 swetismic
 22.044483
59
 0-5-8-17-22
 1-7/5-12/7-11/7-11/10
 jove
 22.044491
60
 0-3-9-17-22
 1-11/9-11/6-11/7-11/10
 utonal
 22.044568
61
 0-5-14-17-22
 1-7/5-9/7-11/7-11/10
 jove
 22.049860
62
 0-8-14-17-22
 1-12/7-9/7-11/7-11/10
 swetismic
 22.049934
63
 0-9-14-17-22
 1-11/6-9/7-11/7-11/10
 swetismic
 22.050019
64
 0-3-15-17-22
 1-11/9-11/8-11/7-11/10
 utonal
 22.055285
65
 0-8-15-17-22
 1-12/7-11/8-11/7-11/10
 unimarvel
 22.055368
66
 0-9-15-17-22
 1-11/6-11/8-11/7-11/10
 utonal
 22.055452
67
 0-5-7-19-22
 1-7/5-8/5-9/5-11/10
 otonal
 22.169974
68
 0-5-13-19-22
 1-7/5-6/5-9/5-11/10
 otonal
 22.172438
69
 0-7-13-19-22
 1-8/5-6/5-9/5-11/10
 otonal
 22.172467
70
 0-5-14-19-22
 1-7/5-9/7-9/5-11/10
 swetismic
 22.174936
71
 0-7-14-19-22
 1-8/5-9/7-9/5-11/10
 unimarvel
 22.174965
72
 0-5-17-19-22
 1-7/5-11/7-9/5-11/10
 werckismic
 22.209463
73
 0-14-17-19-22
 1-9/7-11/7-9/5-11/10
 jove
 22.214319

Hexads

Number
 Chord
 Transversal
 Type
 Hash
1
 0-3-6-9-12-15
 1-11/9-3/2-11/6-9/8-11/8
 rastmic
 15.192640
2
 0-2-5-8-14-17
 1-8/7-7/5-12/7-9/7-11/7
 jove
 17.172789
3
 0-3-9-12-15-17
 1-11/9-11/6-9/8-11/8-11/7
 jove
 17.362021
4
 0-2-5-7-14-19
 1-8/7-7/5-8/5-9/7-9/5
 miracle
 19.044834
5
 0-5-7-12-14-19
 1-7/5-8/5-9/8-9/7-9/5
 unimarvel
 19.055709
6
 0-2-5-14-17-19
 1-8/7-7/5-9/7-11/7-9/5
 jove
 19.357631
7
 0-5-12-14-17-19
 1-7/5-9/8-9/7-11/7-9/5
 miracle
 19.366393
8
 0-3-5-8-17-22
 1-11/9-7/5-12/7-11/7-11/10
 jove
 22.044493
9
 0-5-8-14-17-22
 1-7/5-12/7-9/7-11/7-11/10
 jove
 22.049945
10
 0-3-8-15-17-22
 1-11/9-12/7-11/8-11/7-11/10
 unimarvel
 22.055370
11
 0-3-9-15-17-22
 1-11/9-11/6-11/8-11/7-11/10
 utonal
 22.055455
12
 0-5-7-13-19-22
 1-7/5-8/5-6/5-9/5-11/10
 otonal
 22.172477
13
 0-5-7-14-19-22
 1-7/5-8/5-9/7-9/5-11/10
 unimarvel
 22.174975
14
 0-5-14-17-19-22
 1-7/5-9/7-11/7-9/5-11/10
 jove
 22.214329